Algorithm, Geometry, Graph Theory, Numerical Analysis

Forum for the GRE subject test in mathematics.
Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Algorithm, Geometry, Graph Theory, Numerical Analysis

I have been preparing for the maths subject test using Princeton Review as a rough guide on the level of depth required for each topic. But Princeton Review do not have anything regarding Algorithm, Geometry, Graph Theory or Numerical Analysis. I am not a pure maths major (majored in mathematical economics) and haven't taken Algorithm, Graph Theory or Numerical Analysis. So, I am a little bit lost with regards to the depth required in these topics.

For Algorithm and Graph Theory, I am going to use "Discrete Mathematics" by Norman L. Biggs, 2nd edition covering these topics :

Algorithm : Introduction/basic, Efficiency, Growth rates (big O notation), Comparison, Sorting Algorithm.

Graph Theory : Introduction/basic, Isomorphism of Graphs, Degree of a vertex, Path and Cycles, Trees, Vertex Coloring, Trees and sorting algorithms, Spanning Trees and MST problem, Search (depth-first, breadth-first).

Might be covering too much for Graph Theory if we consider how little questions on graph theory will come out in the test. Also, does anyone have any advice for Geometry and Numerical Analysis? These are listed in the syllabus but I have no idea what is the depth required. Any books to recommend?

bobn
Posts: 61
Joined: Thu Nov 12, 2009 2:59 am

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

You dont need sorting, till big O is enough.
In graph theory you just need definitions and basic facts.
Geometry is one of ignored areas but will turn toughest in test. I advise you to practice basic geometry, lines, triangles, circles importantly, little of quadrilaterals.
Numerical analysis you just need basic methods I will give you exhaustive list later. do ping me

hrmmmmm
Posts: 11
Joined: Thu Nov 12, 2009 10:41 pm

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

Typically graph theory or algorithms might two problems total on the test, so it depends how much time you have to study. It may make sense to just study the intro material and then plan to skip anything harder. I seem to recall seeing sorting somewhere, but that may have been an REA practice test.

If you're not a pure math major, the pure non-calc subjects they seem to go most deeply into are topology and algebra. In algebra you should definitely know the Fundamental Theorem of Finitely Generated Abelian Groups, the basic definitions of popular types of rings. Most of the questions can be done directly from the definitions.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

Regarding Graph Theory : There is a question in the 2005 paper (practice booklet) about Spanning Trees. Is that considered basic material on graph theory? My text (Norman Biggs) puts Spanning Trees pretty deep in the chapter.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

Regarding Geometry :

I have no idea how deep to go. What is the standard syllabus for undergraduate Geometry?

I only know we got to know the properties of inscribed and circumscribed objects.

bobn
Posts: 61
Joined: Thu Nov 12, 2009 2:59 am

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

read schaums-outline-of-geometry. But I would say that is not enough. I need to find out a good book on the same syllabus but some what deep into.

hrmmmmm
Posts: 11
Joined: Thu Nov 12, 2009 10:41 pm

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

Bobn's idea is good. My take on the matter is that much of what is on the test would probably be covered in a calc course that covers analytic geometry but in practice calc courses may not cover it. With that in mind, it may be good to look at a fat calculus book.

In my experience, if you take an undergraduate course in geometry you're probably talking about hyperbolic spherical geometry, projective geometry, automorphisms of the complex plane, etc. Stuff that I have not seen on any practice test. The most advanced geometry stuff I've seen on tests would be one where you get a you a Euclidean geometry problem you're supposed to solve using calc.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

hrmmmmm wrote: Stuff that I have not seen on any practice test. The most advanced geometry stuff I've seen on tests would be one where you get a you a Euclidean geometry problem you're supposed to solve using calc.
I am not allowed to discuss actual test questions but it should be fine to discuss the syllabus I have seen during the test?

I went to the Nov test and there were at least 3 questions covering topics like properties of polygons and properties of geometric objects inscribed or circumscribed within circles or triangles. Are these covered in Schaum's Outline of Geometry?

ETS seriously need to give a more detailed syllabus outline. Like printing a textbook or something!

bobn
Posts: 61
Joined: Thu Nov 12, 2009 2:59 am

Re: Algorithm, Geometry, Graph Theory, Numerical Analysis

hrmmmmm,

I dont think problems from analytic geometry will be tougher in test. Typical geometry ones are teasing, I am non math grad and took Euc. geometry atleast 10years back. I tried couple of books, either they are more advanced with out fundamentals (Dover series) or too fundamental. (Schaums).

But if you think peacefuly you can solve them, but in test, they wont provide you with time, you need practice. To be frank GRE Maths Subject test is just GRE Calc. test, the thing is either you know or not. but not you derive when you want. Its more on memory and practice but not knowledge.